Typically, a pulse combustion apparatus includes a combustion chamber and an exhaust pipe which forms a resonant system with the combustion chamber. The apparatus operates on a cycle in which a fuel charge is admitted to the combustion chamber and ignited. The charge then expands into the exhaust pipe causing a partial vacuum in the combustion chamber, which both assists in drawing in a fresh fuel charge and causes high temperature gas to be drawn back into the combustion chamber from the exhaust pipe. The fresh fuel charge ignites spontaneously thereby establishing the next cycle. Accordingly, operation of the apparatus is self-sustaining after initial ignition. An example of a practial application of this type of apparatus is as a heater, for example in a boiler or for air heating.